Oscillation Match #2a

In the animation below, you control the blue dot.  The red dot and the blue dot will both oscillate.  The red dot follows parameters that are already determined. You set the parameters that determine the motion of the blue dot.  The equation for the motion of the blue dot is given by the equation on the graph.

If you click on the "+" sign next to the slider for time (t) you will find all of the controls for that parameter.  By clicking on the play button (black triangle) for time you can make the animations run on their own.  For the other paramters, you can adjust their values with the sliders.

Manipulate[ Plot[ {.5,1}, {x, -5,5}, PlotRange->{ -1.5,1.5},
  Epilog->{PointSize[0.025],Red,
Point[{3.2 Cos[ 2 Pi t/2.2 + Pi*(-.3)],.5}], 
 PointSize[0.025],Blue, 
Point[{A Cos[ 2 Pi t/T + phase],1}],
    Text["x = A cos[ (2π t/T) + ϕ]",  {0,-.5}, Background->White,
    FormatType->Large],
Text["A = ",  {-4,-1}, Background->White,
    FormatType->Large],
Text[A,  {-3,-1}, Background->White,
    FormatType->Large],
Text["T = ",  {-.5,-1}, Background->White,
    FormatType->Large],
Text[T,  {.5,-1}, Background->White,
    FormatType->Large],
Text["ϕ = ",  {3,-1}, Background->White,
    FormatType->Large],
Text[phase,  {4.2,-1}, Background->White,
    FormatType->Large]
},
        Axes->{True,False}],
{t,0,20 Pi},
        {{A,1,"A"},0,5, .1}, {{T, 1, "T"}, -4, 4, .1}, 
        {{phase, 0, "ϕ"}, -Pi,Pi, Pi/20}]